We present physical properties [redshifts (z), star-formation rates
(SFRs) and stellar masses (Mstar)] of nearly 2000 bright (S850 > 4
mJy) submm galaxies in the ~2 deg2 COSMOS and UDS fields selected with
SCUBA-2 on the JCMT, representing the largest homogeneous sample of
850-um-selected sources to date. We check the reliability of our
identifications, and the robustness of the SCUBA-2 fluxes by revisiting
the recent ALMA follow-up. Considering > 4 mJy ALMA sources, our
identification method has a completeness of ~86 per cent with a
reliability of ~92 per cent, and only ~15-20 per cent of sources are
significantly affected by multiplicity (when a secondary component is
brighter than a third of the primary one). The impact of source blending
on the 850-um source counts as determined with SCUBA-2 is modest;
scaling the single-dish fluxes by ~0.9 reproduces the ALMA source
counts. We find median values of z = 2.40+0.10-0.04, SFR = 287+-6 Mo
yr-1, and log(Mstar/Mo) = 11.12+-0.02. These properties clearly locate
bright submm galaxies on the high-mass end of the `main sequence' of
star-forming galaxies out to z~6, thus suggesting that major mergers are
not a dominant driver of the high-redshift submm-selected population.
Their number densities are also consistent with recent determinations of
the evolving galaxy stellar mass function. Hence, the submm galaxy
population is as expected, albeit reproducing the evolution of the main
sequence of star-forming galaxies remains a challenge for theoretical
models/simulations.